Theory of silicon spin qubit relaxation in a synthetic spin-orbit field

We develop the theory of single-electron silicon spin qubit relaxation in the presence of a magnetic field gradient. Such field gradients are routinely generated by on-chip micromagnets to allow for electrically controlled quantum gates on spin qubits. We build on a valley-dependent envelope function theory that enables the analysis of the electron wave function in a silicon quantum dot with an arbitrary roughness at the interface. We assume the presence of single-layer atomic steps at a Si/SiGe interface and study how the presence of a gradient field modifies the spin-mixing mechanisms. We show that our theoretical modeling can quantitatively reproduce the results of experimental measurements of qubit relaxation in silicon in the presence of a micromagnet. We further study how a field gradient can modify the EDSR Rabi frequency as well as the quality factor of a silicon spin qubit. We show that this strongly depends on the details of the interface roughness. Interestingly, for a quantum dot with an ideally flat interface, adding a micromagnet can give rise to the reduction of the EDSR frequency within some interval of the external magnetic field strength.

Automated summary

In this study, we developed a theory for the relaxation of single-electron silicon spin qubits in the presence of a magnetic field gradient. We successfully reproduced experimental measurements using our theoretical modeling, showing that the presence of a gradient field can modify the spin-mixing mechanisms and the EDSR Rabi frequency of a silicon spin qubit. The effect strongly depends on the details of the interface roughness.